Morphological structuring element decomposition
Computer Vision, Graphics, and Image Processing
Theory of linear and integer programming
Theory of linear and integer programming
A Lower Bound for Structuring Element Decompositions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Decomposition of Convex Polygonal Morphological Structuring Elements into Neighborhood Subsets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Decomposition of Arbitrarily Shaped Morphological Structuring Elements
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Combinatorial Optimization Technique for the Sequential Decomposition of Erosions and Dilations
Journal of Mathematical Imaging and Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
A Combinatorial Optimization Technique for the Sequential Decomposition of Erosions and Dilations
Journal of Mathematical Imaging and Vision
Shape representation based on mathematical morphology
Pattern Recognition Letters
Decomposition of binary morphological structuring elements based on genetic algorithms
Computer Vision and Image Understanding
Note: Decomposition of binary morphological structuring elements based on genetic algorithms
Computer Vision and Image Understanding
Decomposition of arbitrary gray-scale morphological structuring elements
Pattern Recognition
Recursive structure element decomposition using migration fitness scaling genetic algorithm
ICSI'11 Proceedings of the Second international conference on Advances in swarm intelligence - Volume Part I
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A finite subset of ZZ^2 is called a structuring element. A decomposition of a structuring element A is a sequence of subsets of the elementary square (i.e., the 3 x 3 square centered at the origin) such that the Minkowski addition of them is equal to A. Park and Chin developed an algorithm for finding the optimal decomposition of simply connected structuring elements (i.e., 8-connected structuring elements that contain no holes), imposing the restriction that all subsets in this decomposition are also simply connected. In this paper, we show that there exist infinite families of simply connected structuring elements that have decompositions but are not decomposable according to Park and Chin's definition.